Closed form logical error rate approximations for surface codes

2026-05-04

AI Summary

This work addresses the challenge of efficiently evaluating the fault-tolerant performance of surface codes, as traditional approaches rely on computationally expensive simulations or crude extrapolations to estimate logical error rates. The authors propose a novel method that leverages problem symmetries to construct a closed-form approximation of the logical error rate under the assumption of independent and identically distributed physical errors. By integrating combinatorial counting with symmetry analysis and, for the first time, explicitly incorporating measurement errors, the model enables comprehensive comparisons across different error models. This approach eliminates the need for large-scale simulations while delivering rapid and highly accurate predictions of logical error rates across varying code distances and physical error rates, thereby offering an efficient tool for optimizing quantum computer architectures.

Abstract

We propose a novel method to calculate logical error rates in surface codes, assuming independent and identically distributed physical errors. We show how to use our method to analyze hypothetical quantum computers with various configurations and select designs with lower error rates. Currently, this requires expensive classical simulations of quantum decoders for various distances and physical error rates or inaccurate extrapolation from minimal experimental data. Instead, we use the symmetry of the problem to count the configurations that result in a logical error with our novel software. Given a physical error rate, we can deduce the probability of a logical error, to provably good accuracy. We include an analysis of measurement errors to allow a more complete comparison of different surface code implementations.

Problem

• logical error rate
• surface codes
• quantum error correction
• physical error rate
• measurement errors

Innovation

• surface codes
• logical error rate
• closed-form approximation
• symmetry-based counting
• measurement errors